# table of primes between the first 100 squares

In support of Legendre’s conjecture, the following table lists the first hundred square numbers and the prime numbers that are between them. (Of course a single counterexample is enough to disprove).

$n^{2}$ $(n+1)^{2}$ $n^{2}
1 4 2, 3
4 9 5, 7
9 16 11, 13
16 25 17, 19, 23
25 36 29, 31
36 49 37, 41, 43, 47
49 64 53, 59, 61
64 81 67, 71, 73, 79
81 100 83, 89, 97
100 121 101, 103, 107, 109, 113
121 144 127, 131, 137, 139
144 169 149, 151, 157, 163, 167
169 196 173, 179, 181, 191, 193
196 225 197, 199, 211, 223
225 256 227, 229, 233, 239, 241, 251
256 289 257, 263, 269, 271, 277, 281, 283
289 324 293, 307, 311, 313, 317
324 361 331, 337, 347, 349, 353, 359
361 400 367, 373, 379, 383, 389, 397
400 441 401, 409, 419, 421, 431, 433, 439
441 484 443, 449, 457, 461, 463, 467, 479
484 529 487, 491, 499, 503, 509, 521, 523
529 576 541, 547, 557, 563, 569, 571
576 625 577, 587, 593, 599, 601, 607, 613, 617, 619
625 676 631, 641, 643, 647, 653, 659, 661, 673
676 729 677, 683, 691, 701, 709, 719, 727
729 784 733, 739, 743, 751, 757, 761, 769, 773
784 841 787, 797, 809, 811, 821, 823, 827, 829, 839
841 900 853, 857, 859, 863, 877, 881, 883, 887
900 961 907, 911, 919, 929, 937, 941, 947, 953
961 1024 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021
1024 1089 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087
1089 1156 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153
1156 1225 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223
1225 1296 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291
1296 1369 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367
1369 1444 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439
1444 1521 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511
1521 1600 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597
1600 1681 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669
1681 1764 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759
1764 1849 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847
1849 1936 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933
1936 2025 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017
2025 2116 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113
2116 2209 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207
2209 2304 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297
2304 2401 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399
2401 2500 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477
2500 2601 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593
2601 2704 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699
2704 2809 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803
2809 2916 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909
2916 3025 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023
3025 3136 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121
3136 3249 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229
3249 3364 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361
3364 3481 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469
3481 3600 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593
3600 3721 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719
3721 3844 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833
3844 3969 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967
3969 4096 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093
4096 4225 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219
4225 4356 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349
4356 4489 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483
4489 4624 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621
4624 4761 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759
4761 4900 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889
4900 5041 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039
5041 5184 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179
5184 5329 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323
5329 5476 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471
5476 5625 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623
5625 5776 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749
5776 5929 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927
5929 6084 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079
6084 6241 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229
6241 6400 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397
6400 6561 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553
6561 6724 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719
6724 6889 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883
6889 7056 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043
7056 7225 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219
7225 7396 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393
7396 7569 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561
7569 7744 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741
7744 7921 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919
7921 8100 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093
8100 8281 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273
8281 8464 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461
8464 8649 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647
8649 8836 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831
8836 9025 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013
9025 9216 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209
9216 9409 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403
9409 9604 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601
9604 9801 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791
9801 10000 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973
10000 10201 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193
Title table of primes between the first 100 squares TableOfPrimesBetweenTheFirst100Squares 2013-03-22 16:38:20 2013-03-22 16:38:20 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Example msc 11A41